23.12 Rlc series ac circuits  (Page 3/9)

Resonance in AC circuits is analogous to mechanical resonance, where resonance is defined to be a forced oscillation—in this case, forced by the voltage source—at the natural frequency of the system. The receiver in a radio is an RLC circuit that oscillates best at its $f_0$ . A variable capacitor is often used to adjust $f_0$ to receive a desired frequency and to reject others. [link] is a graph of current as a function of frequency, illustrating a resonant peak in $I_{\text{rms}}$ at $f_0$ . The two curves are for two different circuits, which differ only in the amount of resistance in them. The peak is lower and broader for the higher-resistance circuit. Thus the higher-resistance circuit does not resonate as strongly and would not be as selective in a radio receiver, for example.

Power in RLC Series ac circuits

If current varies with frequency in an RLC circuit, then the power delivered to it also varies with frequency. But the average power is not simply current times voltage, as it is in purely resistive circuits. As was seen in [link] , voltage and current are out of phase in an RLC circuit. There is a phase angle     $\varphi$ between the source voltage $V$ and the current $I$ , which can be found from

For example, at the resonant frequency or in a purely resistive circuit $Z=R$ , so that $\text{cos}\varphi =1$ . This implies that $\varphi =0º$ and that voltage and current are in phase, as expected for resistors. At other frequencies, average power is less than at resonance. This is both because voltage and current are out of phase and because $I_{\text{rms}}$ is lower. The fact that source voltage and current are out of phase affects the power delivered to the circuit. It can be shown that the average power is